16,703 research outputs found
Lyapunov Functions Family Approach to Transient Stability Assessment
Analysis of transient stability of strongly nonlinear post-fault dynamics is
one of the most computationally challenging parts of Dynamic Security
Assessment. This paper proposes a novel approach for assessment of transient
stability of the system. The approach generalizes the idea of energy methods,
and extends the concept of energy function to a more general Lyapunov Functions
Family (LFF) constructed via Semi-Definite-Programming techniques. Unlike the
traditional energy function and its variations, the constructed Lyapunov
functions are proven to be decreasing only in a finite neighborhood of the
equilibrium point. However, we show that they can still certify stability of a
broader set of initial conditions in comparison to the traditional energy
function in the closest-UEP method. Moreover, the certificates of stability can
be constructed via a sequence of convex optimization problems that are
tractable even for large scale systems. We also propose specific algorithms for
adaptation of the Lyapunov functions to specific initial conditions and
demonstrate the effectiveness of the approach on a number of IEEE test cases
Data-Driven Approximation of Transfer Operators: Naturally Structured Dynamic Mode Decomposition
In this paper, we provide a new algorithm for the finite dimensional
approximation of the linear transfer Koopman and Perron-Frobenius operator from
time series data. We argue that existing approach for the finite dimensional
approximation of these transfer operators such as Dynamic Mode Decomposition
(DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two
important properties of these operators, namely positivity and Markov property.
The algorithm we propose in this paper preserve these two properties. We call
the proposed algorithm as naturally structured DMD since it retains the
inherent properties of these operators. Naturally structured DMD algorithm
leads to a better approximation of the steady-state dynamics of the system
regarding computing Koopman and Perron- Frobenius operator eigenfunctions and
eigenvalues. However preserving positivity properties is critical for capturing
the real transient dynamics of the system. This positivity of the transfer
operators and it's finite dimensional approximation also has an important
implication on the application of the transfer operator methods for controller
and estimator design for nonlinear systems from time series data
Nonlinear modelling and optimal control via Takagi-Sugeno fuzzy techniques: A quadrotor stabilization
Using the principles of Takagi-Sugeno fuzzy modelling allows the integration of flexible fuzzy approaches and rigorous mathematical tools of linear system theory into one common framework. The rule-based T-S fuzzy model splits a nonlinear system into several linear subsystems. Parallel Distributed Compensation (PDC) controller synthesis uses these T-S fuzzy model rules. The resulting fuzzy controller is nonlinear, based on fuzzy aggregation of state controllers of individual linear subsystems. The system is optimized by the linear quadratic control (LQC) method, its stability is analysed using the Lyapunov method. Stability conditions are guaranteed by a system of linear matrix inequalities (LMIs) formulated and solved for the closed loop system with the proposed PDC controller. The additional GA optimization procedure is introduced, and a new type of its fitness function is proposed to improve the closed-loop system performance.Web of Science71110
Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems
Many modern nonlinear control methods aim to endow systems with guaranteed
properties, such as stability or safety, and have been successfully applied to
the domain of robotics. However, model uncertainty remains a persistent
challenge, weakening theoretical guarantees and causing implementation failures
on physical systems. This paper develops a machine learning framework centered
around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and
unmodeled dynamics in general robotic systems. Our proposed method proceeds by
iteratively updating estimates of Lyapunov function derivatives and improving
controllers, ultimately yielding a stabilizing quadratic program model-based
controller. We validate our approach on a planar Segway simulation,
demonstrating substantial performance improvements by iteratively refining on a
base model-free controller
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